598 



BELL SYSTEM TECHNICAL JOURNAL 



to the left of the source is zero, the left-hand side of the filament being 

 open-circuited. For this case, equations (62) are better written in the form 

 obtained by multiplying through by C~ or C"*" , and the special case in 

 question is then found to be given by 



(65) 



CZ = - 



u 



c~ 



6+ ij 



0: 



C+ = C. 



r • r^ = 



/. + 



1 



6+ 1 



C. 



according to which, life is equal to unity, the magnitude of the hole flow 

 to the left into the open-circuit end is b/{b + 2) times that into the circuit 

 end, to the right; or a fraction b/2(h + 1) of the holes flows to the left, 

 and a fraction (b + 2)/2(6 -f 1) to the right. Thus, for germanium, the 

 hole flow into the open-circuit end is 0.43 as large as that into the circuit 

 end, a fraction 0.30 flowing to the left, and 0.70 to the right. It might be 

 observed that the fractions of the injected holes which flow to the left 

 and right are, in this case, proportional to the total currents C" and C+ 

 of the preceding case, for which there is zero hole flow to the left. 



Another general limiting case for the «-type semiconductor is that for 

 Po small, so that the exponential approximations of Section 3.31 apply. 

 The restriction on the magnitude of P is P < < ^. This restriction obtains 

 if Ct is sufficiently small that C~ and C+ do not differ appreciably. Equa- 

 tion (59) then gives 



(66) G+ - G- = - bf, C, . 



Writing C for C~ and C+ , equations (30) and (46) result in 



Icr = ilVoT^ + c]p' = bc^ 

 [G^ = -hlVc^T^ - C]P'= bc-, 



(67) 



whence, solving for G^ — G and comparing with equation (66), 



(68) P° = bf,c,/Vc?T^. 



In accordance with (67), then. 



(69) 



These are the reduced hole flows to the left and right of the source. 

 While it has been assumed that C( is small compared with C, no re- 

 striction has been placed on C itself. For C small compared witli unity, 

 the equations indicate that the hole flows to the left and right are the 



